Introduction

Well I looked up all the Signed Guides here on this page and I didn't quite agree with any of them. And every of them just show you 1 playstyle of Singed, though he has at least 2 possible playstyles, which I want to show in this Guide. I will give you the playstyle I prefer (that is an AP-Build), though on that route I will give you alternative routes to other playstyles and in consideration of the set-up off the opposite team.

Pros / Cons

Pros for AP-Build:
-High damage ouput through Poison
-One of the best farmers
-Fling becomes a decent Nuke

Masteries + Runes

First to the Masteries:
This one is pretty easy for me. Singed is a tank after all so of course the most points go into defense and utility, the only interesting thing in the attack tree is the AP bonus, so my masteries build looks like this: http://leaguecraft.com/masteries/0003000000000003033000340300102104000000000 The +10 AP at lvl 18 from the attack tree can also be exchanged for more points in defense or utility tree, because these 10 AP wouldn't make any difference in the late game (though the bonus is pretty nice in the early-mid game).
The point in teleport can also be exchanged for Heal or Exhaust or Cleanse(or what ever Summoner spell you chose over Teleport).

From this trees I probably prefer the 4th one because of magic penetration and more movement speed.

Now to the runes:
I always choose AP for blue and red, Mana per level for yellow and movementspeed for quintessence.
Though you also could go only AP on blue, red and yellow and movement speed on quintessence for more damage, also earlier (but you will have more mana probs in the early game(until you can take on the golem)).

If you want him as tank you could also go on mag. res. on blue, armor on red and health on yellow, but I would still use the movementspeed runes for quintessence (Singed lifes and dies (and kills) with movementspeed).

One more option is to choose magic penetration for blue and red, since the poison gets affected by mag. res. too. Though Yellow have no magic penetration runes so there stay with mana per level.

Summoner Abilities

This one is a bit more difficult, though one Summoner ability is a MUST HAVE for Singed: Ghost It gives you a lot of movementspeed for a good amount of time and you even skilled it in the masteries.

The 2nd spell isnt so easy to chose.

General good options: Teleport for quick lane change, for example to an upcoming big creep wave or to jump into a team fight quickly. Cleanse for more survivability (you could also skill it in the masteries when you remove points from Archmage's savvy) Flash for more survivability or to jump into a group fight out of the jungle/grass

Good options for a Tank-build: Heal so you can stay longer on your lane and for more survivability Exhaust for it's blinding and slowing effect that can save your's or your friend's ass Cleanse for more survivability (you could also skill it in the masteries when you remove points from Archmage's savvy)

Good options for an AP-build: Clarity to compensate your mana consume in the early-mid game Ignite mainly because of it's nice side-effect to reduce the target's healing and regeneration by 50% what could lead to your poison doing the kill(the damage of ignite is also nothing to sneeze at with 500 dmg no matter what) Exhaust for it's mag. res. debuff(though then you have to skill it in the masteries) and slowing effect mainly

Spells you definitively not need: Revive You shouldn't die that often and there are really better spells Smite You can kill creeps good/fast enough with your poison
[spell=Rally] Nice spell for a Supporter but you should choose other ones Clairvoyance This spell is also a good Supporter spell but nothing Singed really needs

Items

Now to the Items. Of course Singed is a tank but he can also deal very much damage when you build him on AP but I will give you here both item builds, the AP build and the Tank build (I still prefer the AP build).

AP-Build
You should always start with Sapphire Crystal and 1 mana and health potion, for the best early game and to stay long on your lane. Though if you are pretty confident in your abilities you can also start with Amplifying Tome and 1 potion of your choice. But then you should also upgrade your Amplifying Tome into a Mejai's Soulstealer pretty quickly (before you buy the next items).

For the next item you either build a Archangel's Staff or a Lich Bane what you prefer more.
With Archangel Staff you wont have any mana problems more in the game and Lichbane gives a nice speed boost and unique ability that works good with your ultimate.

Mostly now the game should be over, but if it's a long game you can build the other item you didn't build before from the two next. And if it's a really long game then you add 1 [item=Zhonya's Ring] and a 2nd Archangel's Staff.

Now I started to test a 3rd AP-Build that heavily supports your poison but has around 200 AP less than the other 2.

Now you start to build [item=Rylai's Scepter], it doesnt mater with which component you start. Rylai's is nice because you poison will slow too when you have it.
When you have your Rylai's Scepter you can go for a Void Staff mainly for the magic penetration so that your poison can make the kill also in late game.
If the game isnt over yet you can start to build Archangel's Staff and [item=Zhonya's Ring], in this order.

No matter what purchase as 2nd upgraded-item after the Boots your Warmog's Armor, so that you have enough time to build up it's passive. After that you can go for a Catalyst the Protector and upgrade it as soon as possible into a Banshee's Veil and upgrade your Boots of Speed (even before your Warmog's) into Mercury's Treads (though if there are mainly physical DDs and few CCs you also can upgrade them to Ninja Tabi) this way you have some nice survivability pretty early. If you don't see the need of one of these 2 boots you also can go with Boots of Swiftness they are never wrogn in a Singed Build ;).

When you finished Banshee's you start with [item=Force of Nature] if you started without Leviathan and a Frozen Heart or Guardian Angel if you started with Leviathan.

The game shouldn't last that long but if so, then after Force of Nature (if you chose that path) you build Frozen Heart and Guardian Angel which order doesnt really matter. And the path with Leviathan builds the item that wasnt build in the previous step.

Skilling Order

Skill this way (if want to have more damage earlier):

or this way(if you go more on teamplay):

Farming

Farming is pretty easy. You toggle your Poison Trail and start to go around and through the creeps, though don't let it on all the time because, especially in the early game, it is really mana consuming.(though in the late game and with golem or nashor buff or ulti activated it has as good as no mana cost (the mana renegates faster than is used up))

Creep Jungling

Almost the same like Farming so you can throw one of the harder monsters to beat over your shoulder now and then, but make sure they stay in your poison.

Working in the team

Working in the team is really great for Singed because here he shows his best capabilities. If you want to focus on someone of the opposing team, throw your Mega Adhesive to his feets rush in fwith ghost/ultimate or both and use Fling on him to throw him into your allies. And dont forget to activate Poison Trail before that.

So you see you can be a very good initiator but with Fling you can also save your teammates asses, when they getting attacked you fling the opponent away from your teammate and use Mega Adhesive to slow them down.

And you should also not forget that Fling can interrupt some ultimates like Nunu's Absolute Zero or Katarina's Death Lotus or Warwick's Infinite Duress, so you can save your and your teammates' asses when flinging these guys while they do their ulti.